I'm having trouble solving the following number theory problem in my textbook:
Let a $\in Z$ with $a > 0$. Prove that there exists $k, n \in Z$ with n odd such that $a = 2^k n$
So far I've tried writing $n$ as an odd integer (i.e. n = 2q + 1) and then reducing somehow but that doesn't seem to be the correct way to solve it because I can only prove that $a$ can be even and not odd.
Any help would be appreciated?